Finite Group DatabasebetaFinite Group Databasebeta| order | 6700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic335 |
| unambiguous semidirect product | C67⋊(C5×Dic5) |
| derived | C5×C67 ⋊ C4×C5 |
| Hall | C52×C67 ⋊ C4 |
| Sylow | C67 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D335 |
| commutator, hypocenter | C5×C67 | C4×C5 |
| Frattini | C2 | C5×D335 |
| Fitting, socle | C2×C52×C67 | C2 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 ◁ C2×C5 | |
32 conjugacy classes of subgroups.
1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×(C67⋊C3)⋊Dic5, C67⋊#64470, C5×Dic1005, … |
| maximal normal subgroup of | C5×(C67⋊C3)⋊Dic5, C3×C5×Dic335 |
| maximal quotient of | C5×Dic1005, C3×C5×Dic335 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6700, 15);